Dynamic PCA Fault Detection Using Principal Component Pursuit
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Solution Overview
Problem
Existing fault detection methods in industrial processes, such as those in hydrocarbon facilities, are inadequate in handling imperfect training data and real-time processing of large-scale time-sequence data sets, leading to errors and inefficiencies in sensor data analysis.
Innovation Solution
A computer-implemented method and system that performs principal component pursuit on a data matrix to form an uncorrupted matrix, followed by dynamic principal component analysis, allowing for fault detection and correction or sensor repair in industrial processes with time-series data from multiple sensors.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional PCA or DPCA is used for fault detection, then the method is computationally simple and easy to implement, but it cannot handle missing or corrupted data in the training data set
Solution Approach 1:
The patent segments the data processing into two distinct phases: (1) an offline training phase where PCP is performed on training data to create a robust model that can handle corrupted data, and (2) an online detection phase where the pre-trained model is applied to new data for fault detection. This segmentation allows the complex PCP computation to be performed only once during training, while maintaining high reliability during real-time operations.
Solution Approach 2:
The patent performs preliminary data cleaning and model training using Principal Component Pursuit (PCP) before actual fault detection. The PCP algorithm is applied offline to decompose the training data matrix into low-rank (clean) and sparse (corrupted) components, creating a pre-processed training set that is free from the influence of corrupted data. This preliminary action ensures that the subsequent DPCA model is trained on clean data, improving fault detection reliability without requiring real-time data cleaning.
2Reliability
If PCP analysis is used for fault detection on real-time data, then it can handle corrupted data, but it is computationally complex
Solution Approach 1:
The patent divides the computational workload by segmenting PCP application to only the offline training phase, while using computationally lighter DPCA for online real-time fault detection. The complex convex optimization of PCP is performed once during model training, and the resulting robust DPCA model is then applied efficiently to streaming data, achieving both high reliability and low real-time computational complexity.
Solution Approach 2:
The patent performs the computationally intensive PCP analysis as a preliminary offline step to prepare clean training data and train a robust DPCA model. By completing the heavy computational work beforehand, the system achieves high fault detection reliability while maintaining low computational requirements during real-time operations, where only lightweight DPCA computations are needed.
3Measurement precision
If manual data cleaning is performed to prepare fault-free training data, then the model accuracy improves, but it is time-consuming
Solution Approach 1:
The patent replaces manual mechanical data cleaning with an automated algorithmic approach using Principal Component Pursuit (PCP). The PCP algorithm automatically identifies and separates corrupted data points from clean data through mathematical decomposition, eliminating the need for time-consuming manual inspection and cleaning while achieving superior model accuracy. This substitution of automated computation for manual labor dramatically reduces data preparation time.
Solution Approach 2:
The patent implements self-service data cleaning where the PCP algorithm automatically identifies, isolates, and removes corrupted data points without human intervention. The algorithm performs self-diagnosis of data quality issues and self-cleanses the training set by decomposing it into low-rank (clean) and sparse (corrupted) components, achieving both high model accuracy and rapid data preparation.
4Productivity
If DPCA model is built using corrupted training data, then the modeling process is faster, but the detection accuracy decreases
Solution Approach 1:
The patent performs preliminary data cleaning using PCP before building the DPCA model, ensuring that the training data is free from corrupted values. This preliminary action of automated data cleansing maintains fast modeling speed by eliminating manual cleaning steps, while simultaneously improving detection accuracy by ensuring the model is trained on clean data. The PCP-based preprocessing is computationally efficient and seamlessly integrates into the modeling workflow.
Data Source
AI summary
Methods and systems for detecting a fault in a data set from an industrial process are disclosed. One method includes forming a first data matrix at a data processing framework from time-series training data, and performing a principal component pursuit on the first data matrix to form an uncorrupted, unscaled matrix and a sparse matrix in the memory, and scaling the uncorrupted, unscaled matrix to form an uncorrupted scaled matrix. The method also includes performing a dynamic principal component analysis (DPCA) on the uncorrupted scaled matrix to form a DPCA model, and determining a squared prediction error from the DPCA model. Based on the squared prediction error, faults are detected in a different data set from operation of the industrial process. At least one of (1) correcting the one or more faults in the different data set or (2) performing a repair operation on a sensor is performed.